How to know if a filter fits to my lens?

Hi
i have a nikon d3100 and a 18-55, 55-200 lenses. If i buy a uv, and, polarizer filters of 52 mm would they fit to both lenses?

On the front of the lens will be marked the filter size, if the sizes are different you can get step rings always go for the larger size to step down

The front of the lens will show xxΦ (52Φ, 58mmΦ, etcetera).

That is the filter and cap size for that particular lens in millimeters.

Camera filters are a simple and inexpensive way to add effects to basic camera lenses. Filters come in the same sizes as lenses. If your lenses are 35 mm, then 18 to 35 mm filters will fit. The same rule applies if the lenses measured are 12 mm, then you know 11 to 18 mm lenses would fit and so on. The only tricky part is finding out the size of your lenses. Follow these helpful steps.

1. Look at the side of the lens. On any SLR or point and shoot lens, the size should have the size written on the lens. If not, look at the front of the lens. It should read a number like 18 to 35 mm or 17 to 55mm and so on.

2. If you can't find the number on the lens, get a piece of string and hold it across the front glass part of the lens. Mark the sides of the string.

3. Measure the marked string by millimeters. If you only have metric ruler, here's a cheat sheet: 1 inch equals 2.54 cm; 1 cm equals 10 mm and 1 inch equals (2.54 x 10) mm equals 25.4 mm. The number you get, say your lens is 35 mm across, that is the number that you will use for sizing.